Condorcet's jury theorem states that given two alternative decision of which one is correct. If the average probability of voters to arrive at the correct decision is more than 50% the more voters are added to the sample the more likely the correct decision is made. On the other hand, if the average probability to vote correctly is less than 50%, the more voters the less likely a correct outcome.

The limitations are correctly discussed on the Wiki page and the mathematical model of democratic election add its own perspective [1], I feel a historical perspective is worth mentioning here.

Condorcet's jury theorem

My model calculations

Deals with two distinct states only true and false

Considers a whole spectrum of capabilities

Makes claims about the outcome if the probability of a correct decision is less or more than 0.5

Considers a random function of probabilities. The value of this function is defined by an individual's own capabilities

In summary the model provided by the above mentioned publication offers a generalization of Condorcet's jury theorem.

Historical Implications

Condorcet's theorem (1785) played a pivotal role in establishing majority decisions as a tool to improve political decision making. As his theorem proved that a jury is more likely to find the right decision compared to a single person, this theorem served as a mathematical prove for the necessity of he French Revolution (1789–1799) that that removed the rule of a few aristocrats and established a democratic rule of the people in place of it. My model serves the same purpose. It also demonstrates that a democratic election is superior to just a single aristocrat's decision, as it always ensures a slightly better than average decision maker, which does not hold true for an aristocrat who inherited his position and who definitely can be more stupid than average.

Today we realize that democratic elections are far from optimal. Not only the political decision makers tend to please their voter by exaggerated gifts, but also the election process itself becomes a target of manipulation and fraud. Therefore my model has been developed to mathematically explain all these pitfalls to help preventing them.